A telescope has an objective lens of focal length `200cm` and an eye piece with focal length `2cm`. If this telescope is used to see a 50 meter tall building at a distance of `2km,` what is the height of the image of the building formed by the objective lens?

Options

A. `5` cm
B. `10` cm
C. `1` cm
D. `2` cm

Answer

A

Explanation

For objective lens, `f_(0)=+200` cm,
`u_(0)=-2xx10^(5)` cm
For a lens
`(1)/(v_(0))-(1)/(u_(0))=(1)/(f_(0))` or `(1)/(v_(0))=(1)/(f_(0))+(1)/(u_(0))=(1)/(200)-(1)/(2xx10^(5))=(999)/(2xx10^(5))`
or `v_(0)=(2xx10^(5))/(999)` cm
Consider magnification due to objective lens
`:.("Size of image")/("Size of object")=|(v_(0))/(u_(0))|`
`:. "Size of object" = "size of object" xx|(v_(0))/(u_(0))|`
`=(50xx100)xx(2xx10^(5))/(999)xx(1)/(2xx10^(5))=(5000)/(999)` cm `=5` cm